# Lesson 10

Using Data Displays to Find Associations

### Lesson Narrative

In this lesson, students use two-way tables, bar graphs, and segmented bar graphs to decide whether there is evidence of an association in categorical data or not (MP4).

### Learning Goals

Teacher Facing

• Create a two-way table and a segmented bar graph that represent relative frequencies, and interpret (orally) the frequencies in context.
• Determine (in writing) whether categorical data has a positive, negative, or no association using a relative frequency table or segmented bar graph, and justify (orally) the reasoning.

### Student Facing

Let’s use data displays to find associations.

### Required Preparation

Use the data from the previous lesson’s cool-down to build a two-way table of students’ responses. Provide access to materials for students to create their own segmented bar graphs including colored pencils and straightedges.

### Student Facing

• I can create relative frequency tables, bar graphs, and segmented bar graphs from frequency tables to find associations among variables.

### Glossary Entries

• relative frequency

The relative frequency of a category tells us the proportion at which the category occurs in the data set. It is expressed as a fraction, a decimal, or a percentage of the total number.

For example, suppose there were 21 dogs in the park, some white, some brown, some black, and some multi-color. The table shows the frequency and the relative frequency of each color.

color frequency relative frequency
white 5 $$\frac{5}{21}$$
brown 7 $$\frac{7}{21}$$
black 3 $$\frac{3}{21}$$
multi-color 6 $$\frac{6}{21}$$
• segmented bar graph

A segmented bar graph compares two categories within a data set. The whole bar represents all the data within one category. Then, each bar is separated into parts (segments) that show the percentage of each part in the second category.

This segmented bar graph shows the percentage of people in different age groups that do and do not have a cell phone. For example, among people ages 10 to 12, about 40% have a cell phone and 60% do not have a cell phone.

• two-way table

A two-way table provides a way to compare two categorical variables.

It shows one of the variables across the top and the other down one side. Each entry in the table is the frequency or relative frequency of the category shown by the column and row headings.

A study investigates the connection between meditation and the state of mind of athletes before a track meet. This two-way table shows the results of the study.

meditated did not meditate total
calm 45 8 53
agitated 23 21 44
total 68 29 97